Movies for Partial Differential Equations

Transport equation:   ut + ux = 0

            

 

 

Heat equation:   Dirichlet boundary conditions

            

 

 

Heat equation:   periodic boundary conditions

            

 

 

Heat equation:   denoising

            

 

 

Wave equation:   Particles and Waves


The movies show the solution u(t,x) = cos t sin x = (sin(x-t) + sin(x+t))/2
The first movie is the solution in its first, wave form;
The second movie shows the two constitutent traveling waves (like particles);
The third movie plots them together.

            

 

 

Wave equation:   Interaction of waves

            

 

 

Wave equation:   Dirichlet boundary conditions

            

 

 

Wave equation:   Odd periodic extension

            

 

 

Wave equation:   Hammer blow, Dirichlet boundary conditions

            

 

 

Wave equation:   Hammer blow, Neumann boundary conditions